I have the following question, we were given an equation involving and where you use the two options to create two equations from the given payoffs. However because the payoff for the option when the stock decreases, is greater than the payoff for the higher valued stock, it leads to negative -1/3 for and then a value of 1.4.... for . this prices the derivative option at a negative value, however this isn't possible as their is guaranteed no loss on the option, hence it must have a price above zero

A derivative on a stock will expire exactly 6 months from now.

The payoff of the derivative is given by:

Payoff = 120 - S_Tif S_T 120

= S_T - 120if S_T > 120

where S_T denotes the price of the stock on the expiry date.

The stock price today is 100.

On the expiry date, the stock price is expected to be either 140 or 80.

The annual interest rate is 10% and compounded continuously.

Using a two period model, find the price of the derivative.

Explain all your steps clearly.